Abstract: The existing reliability calculation methods of random stress and fuzzy strength have been systematically studied, and divided into four categories: method of directly transforming fuzzy variables into random variables, method of directly constructing membership functions of fuzzy failure events from that of fuzzy strength, possibility method and practical calculation method. Moreover, they can also be simply classified as quantitative calculation methods and fuzzy calculation methods due to the attribute of fuzzy failure probability. As for the quantitative calculation methods, the generalized density function method and equivalent density function method are, respectively, equivalent to the area method and cut set method. Under such circumstances, it can be concluded that the really independent methods for the quantitative calculation methods only include the generalized density function method, the equivalent density function method and the direct transformation method. Relevant formulas are derived for the cases where the fuzzy membership function of strength follows linear or normal distribution. The numerical results of common methods are comparatively studied, where the significant differences between each other indicate that the most reasonable method need to be further studied.